A unified similarity transformation for Darcy and non-Darcy forced-, free- and mixed-convection heat transfer in non-newtonian inelastic fluid-saturated porous media

A unified similarity transformation has been proposed which can deduce a class of possible similarity solutions during forced-, free- and mixed-convection flow of non-newtonian inelastic fluids through porous media under Darcy and non-Darcy conditions. The velocity scale using the slip velocity at the wall under mixed-convection flow has been utilized for generating a modified Peclet number which correctly transforms to the appropriate Peclet and Rayleigh numbers under limiting conditions. The unified approach is seen to reveal the existence of three limiting regimes lined by forced convection, Darcy free convection and Forchheimer free convection together with three intermediate regimes of Darcy mixed convection, Darcy-Forchheimer free convection and Forchheimer mixed convection. Exact solutions have been found for each of the regimes and the effects of non-newtonian character on the heat transfer characteristics have been deciphered.